EE 3410 Electric Power
Homework 3
Deadline: March 6, 11:59 pm
Problem 1:
In the circuit shown below, the voltage of phase 𝑎𝑎 of the voltage source is 12,000 + j0 V. Assume the positive phase sequence. The
balanced source produces 1.5 MW and 0.3 MVAR. Calculate:
a) Line current (20 pts)
b) 𝑍𝑍𝑝𝑝 (20 pts)
Aa
15
A
Vcn
Nn
ZP
Vbn
+
VCA
VAB
+
+VBC
15
Bb
ZP
Van
ZP
B
C
15
Problem 2:
A voltage of 𝑉𝑉𝑎𝑎𝑎𝑎 = 1∠0 KV negative sequence (balanced) is available at a factory. We have 𝑍𝑍1 = 50 + 𝑗𝑗50, and 𝑍𝑍2 = 60 − 𝑗𝑗20.
a) Calculate 𝑉𝑉𝑎𝑎𝑎𝑎 , 𝑉𝑉𝑏𝑏𝑏𝑏 , 𝑉𝑉𝑐𝑐𝑐𝑐 , 𝑉𝑉𝐴𝐴1𝐵𝐵1 , 𝑉𝑉𝐵𝐵1𝐶𝐶1 , 𝑉𝑉𝐶𝐶1𝐴𝐴1 , 𝑉𝑉𝐴𝐴2𝑁𝑁 , 𝑉𝑉𝐵𝐵2𝑁𝑁 , 𝑉𝑉𝐶𝐶2𝑁𝑁 (10 pts)
b) Calculate 𝐼𝐼𝑎𝑎𝑎𝑎 , 𝐼𝐼𝑏𝑏𝑏𝑏 , 𝐼𝐼𝑐𝑐𝑐𝑐 , 𝐼𝐼𝐴𝐴𝐴𝐴1 , 𝐼𝐼𝐵𝐵𝐵𝐵1 , 𝐼𝐼𝐶𝐶𝐶𝐶1 , 𝐼𝐼𝐴𝐴𝐴𝐴2 , 𝐼𝐼𝐵𝐵𝐵𝐵2 , 𝐼𝐼𝐶𝐶𝐶𝐶2 (10 pts)
c) Calculate 𝐼𝐼𝑁𝑁𝑁𝑁 (5 pts)
d) Draw a three-phase voltage phasor diagram corresponding to the Y-connected load (5 pts)
e) Draw a three-phase current phasor diagram corresponding to the Y-connected load (5 pts)
f) Calculate the instantaneous active power generated by the source at time 𝑡𝑡 = 1000 seconds (10 pts)
g) Calculate complex power consumed by loads 𝑍𝑍1 and 𝑍𝑍2 (5 pts)
h) Calculate the complex power generated by the source (5 pts)
j) Calculate the power factor from the source’s perspective (5pts)
a
A
+
Z2
2Ω
_
n
_
A2
_ +
b
N
B2
B
+
C
c
A1
Z1
B1
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Z1
Z1
C1
Z2
Z2
C2